As conservatives gather in the Washington area on Thursday for three days of speeches from prospective 2016 presidential candidates and discussions about the future of the GOP, a new Washington Post-ABC News poll found that three in 10 of all Republicans say they would not vote for New Jersey Gov. Chris Christie if he ran for the White House.

Christie addressed the annual Conservative Political Action Conference on Thursday morning. He was not invited to speak at last year’s event. What he said and the reception he received will be closely watched and analyzed, and the new survey underscores the obstacles Christie will face if he seeks his party’s nomination in 2016.

The poll also found that former Florida governor Jeb Bush has problems of a different kind. He is more popular in the Republican Party than Christie but faces potential head winds as a candidate. The Post-ABC poll found that almost half of all Americans, and 50 percent of registered voters, say they “definitely would not” vote for him for president — a possible hangover from the presidency of his brother George W. Bush.

The overall findings underscore the degree to which the contest for the GOP nomination in 2016 is as wide open as any in the modern era. The poll found that there is no obvious beneficiary to Christie’s problems within the party or Jeb Bush’s apparent problem with the wider elec­torate. Many of those thinking about running have made little impression on the general public and in some cases they are not even well known among Republicans.

The survey asked about nine Republicans, most of them thinking seriously about running in 2016, and one Democrat, Hillary Rodham Clinton. Twenty-five percent of all Americans say they “definitely would” vote for the former secretary of state, while 41 percent say they would consider doing so. Thirty-two percent of all Americans (and 37 percent of registered voters) say they definitely would not.

Christie’s fortunes have ebbed and flowed over the past few months. After winning re­election handily in the fall, the governor was touted as the favorite of the GOP establishment to lead the party in 2016. He was considered a straight-talking Republican who knew how to attract support in a heavily Democratic state.

Since then, he has been badly damaged politically by the controversy over a four-day traffic snarl in September that appears to have been ordered by his aides and advisers as political retribution. Christie fired those directly involved and said he had no direct knowledge of the incident when it happened. He is facing two investigations, one by the state legislature and the other by U.S. Attorney Paul Fishman.

The poll does not provide information that could distinguish how much Christie’s problems are a result of the controversy and how much they reflect general skepticism toward him among conservatives.

Just 9 percent of Republicans say they definitely would vote for Christie, while 50 percent say they would consider doing so. Eleven percent say they have no opinion.

The 30 percent of Republicans who say they definitely would not vote for Christie is the highest percentage for any Republican tested. Next was former Arkansas governor Mike Huckabee, at 24 percent, followed by 2012 GOP presidential nominee Mitt Romney at 23 percent, Texas Gov. Rick Perry at 21 percent, Sen. Ted Cruz (Tex.) at 20 percent and Bush at 18 percent.

Romney has the most definite support among Republicans, at 34 percent, followed by Bush and Huckabee at 15 percent each. Two other Republicans, Sens. Marco Rubio (Fla.) and Rand Paul (Ky.), scored in the low double digits on the percentage of Americans who say they definitely would vote for them.

Wisconsin Gov. Scott Walker has the lowest percentage (12 percent) of Republicans saying they definitely would not vote for him, but he is by far the least known of the group within the party, with nearly a third of all Republicans saying they have no opinion about him as a presidential candidate.

The poll did not pit Republicans against one another, nor did it test hypothetical general-election matchups between individual Republicans and Clinton. The survey also is not a definitive gauge of how people would vote in the GOP primaries or the general election. But as one early indicator, the findings help to stratify the field of candidates and give some sense of the breadth or depth of interest voters have at this point.

Among conservative Republicans, who make up about two-thirds of the party and who play a significant role in primaries, Christie’s problems are more acute. Just 8 percent of them said they definitely would vote for Christie for president. Only Perry fared worse, at 7 percent.

Romney received the strongest backing from conservative Republicans, with 37 percent saying they definitely would support him. Trailing him were Huckabee, Bush, Paul, Rubio, Walker and Cruz, who all stood between 19 percent and 11 percent of firm support. Other than for Romney, Huckabee and Paul had the most solid backing among Republicans who described themselves as “very conservative.”

Meanwhile, Christie topped the list of candidates who conservative Republicans said they definitely would not support, with 35 percent of that group saying so. Disaffection with the governor among conservative Republicans was far higher than for any other potential candidate tested, with Huckabee next, at 22 percent.

Talk about a possible Bush candidacy increased significantly early this year, particularly among establishment Republicans, in part because of the controversies that have set back Christie. That has fed talk that he is now leaning more toward running than he once was.

Bush has said for more than a year that he would look seriously at whether to run later this year. Friends say nothing has changed, that running always has been a possibility and remains so, but that the decision could go either way. He has said that his decision will depend on family considerations and whether he has the passion required to run and serve.

“The early narrative probably underestimated how seriously he would consider it and the current narrative is overanalyzing where he is in the process and what he may do,” said one person close to Bush.

The findings on Clinton add more data to the emerging picture of a candidate, should she decide to run, who would begin the 2016 campaign stronger than she had in 2008. At this point in 2006, 42 percent of the public said they definitely would not vote for her, while 19 percent said they definitely would.